[Proj] How grids work in PROJ4

J. Luis jmfluis at gmail.com
Wed Jan 11 20:57:40 EST 2012

> Michal,
> I have checked.  At a point like -116,39 the egm96_15.gtx file has a
> value of approximate -21.  At that location the geoid is around 21
> meters above the ellipsoidal height.  So the value in the .gtx file is
> the amount (in meters) that should be added to the geoid to get to
> the ellipsoidal height.
> When the geoidgrid is on the left side (the source coordinate system)
> the input height is assumed to be geoidal and the amount in the
> gtx is added to get to ellipsoidal height.  When the right side
> (destination coordinate system) has a geoidgrids setting the value
> read from the gtx is subtracted from the elevation to get back to
> geoidal height.
>> As I know it is usual there is positive value in geoid data set in case
>> geoid is above ellipsoid.
> Your statement does not match with my findings.  I expect the opposite.
> I will note I am using the same convention (positive vs. negative) as
> I encountered with the .gtx files distributed with the VDatum program.


I don't know what type of altitude is assumed to be the left/right side 
but there is no doubt that when the geoid is above the ellipsoid the so 
called geoid undulations or anomalies are positive and negative when 
they are bellow. It should be better to call the altitudes as they are 
know in geodesy.

- The ellipsoidal distance is the distance to the ellipsoid - usually 
denoted by 'H'
- Orthometric distance is the distance along the plumb line from a point 
and the geoid - usually called 'h' and is what we simply call 'altitude'
- Geoid undulation is the distance between the geoid and the ellipsoid - 
called 'N'

the relation between the three is

h = H - N

We can see it pictorially here 

If that matters (and it should) the point -116 39 according to the egm96 
geoid has an geoid anomaly (or geoid height) of -22.02 and not -21. 
Though, -21 is more close to value given by the egm2008 geoid, which is 
-21.60. One get check those values here
that is computed using the free geographicLib


>> Also egm96_15.gtx is done like this. Should it
>> be inverted in case of proj library?
>> Example:
>> PROJ_LIB=nad PROJ_DEBUG=ON  src/cs2cs +proj=latlong +ellps=WGS84
>> +towgs84=0,0,0 +geoidgrids=egm96_15.gtx +to +proj=latlong +ellps=WGS84
>> +towgs84=0,0,0
>> 15d 50d 0
>> 15dE    50dN 44.690
>> PROJ_LIB=nad PROJ_DEBUG=ON  src/cs2cs +proj=latlong +ellps=WGS84
>> +towgs84=0,0,0 +to +geoidgrids=egm96_15.gtx +proj=latlong +ellps=WGS84
>> +towgs84=0,0,0
>> 15d 50d 0
>> 15dE    50dN -44.690
> I checked in the area of 15E, 50N and the .gtx value was approximately
> +45 in the .gtx file.
> Best regards,

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